Average Error: 14.9 → 0.4
Time: 7.3s
Precision: binary64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \left(\sin b \cdot \frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a}\right)\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \left(\sin b \cdot \frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a}\right)
double code(double r, double a, double b) {
	return (((double) (r * ((double) sin(b)))) / ((double) cos(((double) (a + b)))));
}
↓
double code(double r, double a, double b) {
	return ((double) (r * ((double) (((double) sin(b)) * (1.0 / ((double) (((double) (((double) cos(b)) * ((double) cos(a)))) - ((double) (((double) sin(b)) * ((double) sin(a)))))))))));
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 14.9 bits

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]

  2. SimplifiedError: 14.9 bits

    \[\leadsto \color{blue}{r \cdot \frac{\sin b}{\cos \left(b + a\right)}}\]
  3. Using strategy rm

  4. Applied cos-sumError: 0.3 bits

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}}\]
  5. Using strategy rm

  6. Applied div-invError: 0.4 bits

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a}\right)}\]

  7. Final simplificationError: 0.4 bits

    \[\leadsto r \cdot \left(\sin b \cdot \frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a}\right)\]

Reproduce

herbie shell --seed 2020200 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))